Bifurcation of limit cycles from the global center of a class of integrable non-Hamilton system under perturbations of piecewise smooth polynomials

2019/04/11 by Shiyou Sui, Sui, Shiyou, Liqin Zhao +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Lipid metabolism and biosynthesis #Microtubule and mitosis dynamics

paper · pdf · doi:10.48550/arxiv.1904.05702

openalex publication_date 2019/04/11 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28

Abstract

In this paper, we perturb the global center of the planar polynomial vector fields X(x,y)=(-y(x²+a²),x(x²+a²)) (a≠0) inside cubic piecewise smooth polynomials with switching line y=0. By using average function of first order, we prove that the sharper bound of the number of limit cycles bifurcating from the period annulus is 6.

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